feat(profile)!: replace sidebar and add avatar navigation

Rename the global Sidebar route, UI, assets, analytics, and payment return context to Profile. Add accessible message-avatar navigation and preserve the source character across auth and logout flows.

BREAKING CHANGE: /sidebar has been removed; use /profile instead.

src/router/route-meta.ts

@@ -15,7 +15,7 @@ const GLOBAL_ROUTE_ACCESS: Partial<Record<string, RouteAccess>> = {
   [ROUTES.privateRoom]: "guestEntry",
   [ROUTES.tip]: "public",
   [ROUTES.externalEntry]: "public",
-  [ROUTES.sidebar]: "session",
+  [ROUTES.profile]: "realUser",
   [ROUTES.feedback]: "session",
   [ROUTES.subscription]: "realUser",
   [ROUTES.coinsRules]: "public",